Learning monomials help in understanding complex polynomial expressions. It is the most basic form of the polynomial used in everyday life for managing finance, accounts, business, and more. Monomial is a polynomial with only one term. Learning to simplify monomials is necessary to attain the fluency to solve complex polynomial expressions. Simplifying monomials requires understanding various rules and operations based on handling exponents, multiplication, and division. It also requires a clear understanding of various terms related to monomials and operations involved in simplifying them. Let us start with understanding what monomials are.
What is a Monomial?
A monomial is a polynomial expression with variables and a coefficient. It does not include addition or subtraction. An example of a monomial is 7x; this expression has only one term. Other examples of a monomial are 4(constant ), or a variable z, product of number and variable, i.e., 5x, or product of number and variable with an exponent like 9x².
Degree of a Monomial:
The degree of a constant monomial is zero. If the polynomial contains only a constant value such as 35 or 50, then the degree of this type of monomial is zero. You can also consider this monomial as the constant term attached to a variable with the power of 0, which is 1. Consider the monomial 10; you can think of it as 10x^0, 10 x 1, or 10; Which implies that the degree of a constant monomial is 0.
The degree of a monomial with one variable is the number in the exponent of the variable. For example, the degree of monomial 3x^2 is ‘2’. The degree of a monomial with more than one variable is the sum of the exponents of the variables in the term. For example, the degree of monomial 3x^2 y is ‘3’ since the power of ‘x’ is two and ‘y’ is one.
Definitions of Terms
The base is a variable, and an exponent is a power a variable is raised to. A variable that has no visible exponent is assumed to have an exponent ‘1’. The coefficient of a monomial is a number preceding a variable; for example, in 7y, the 7 is the coefficient.
Let us consider a monomial expression: 6x^3 y.
In this monomial, ‘x’ and ‘y’ are the variables with exponents 3 and 1. So the degree of this monomial is ‘4’.
A variable with no visible exponent like y is assumed to have an exponent of 1.
The coefficient is ‘6’, and the literal part is x ^3 y.
What are Similar monomials?
Two monomials are said to be similar if they both have the same literal part. For example, 2xy^2 and xy^2 have the same literal part and can be added or subtracted from each other. Two similar monomials can be simplified by applying arithmetic operations such as addition, subtraction, multiplication, and division.
Rules for Simplifying Monomials
Simplification of monomials is a process that follows a sequence of operations, including rules to handle exponents, multiplication, and division. Learning this skill requires a basic understanding of monomials and rules to simplify them. Here are some rules to simplify monomials:
- The power of a power rule states that when evaluating the power of a power, multiply the exponents of base variables.
- The multiplication rule of monomials states that while multiplying the monomial expressions, add the exponents with like bases.
- The dividing monomials rule states that when you divide monomials, subtract the exponents of like bases.
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